To guarantee especially in exhaust systems used in connection with diesel internal combustion engines that the increasingly strict legal requirements imposed on the emission of pollutants, especially on the emission of nitrogen oxides, can be met, a reactant, for example, a urea/water solution, is injected into the exhaust gas flowing in such exhaust systems. The nitrogen oxides contained in the exhaust gas are converted with the ammonia contained in the reactant into water and nitrogen by means of a selective catalytic reduction in an SCR catalytic converter device arranged downstream of the reactant injection area.